The algebraic classification (up to isomorphism) of algebras of dimension \(n\)  from a certain variety
defined by a certain family of polynomial identities is a classic problem in the theory of non-associative algebras.
There are many results related to the algebraic classification of small-dimensional algebras in the varieties of
Jordan, Lie, Leibniz, Zinbiel and many other algebras [1]}, [2]}, [3]}.
Geometric properties of a variety of algebras defined by a family of polynomial identities have been an object of study since 1970's (see, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}).
Gabriel described the irreducible components of the variety of 4-dimensional unital associative algebras [11]}.
Cibils considered rigid associative algebras with 2-step nilpotent radical [12]}.
Grunewald and O'Halloran computed the degenerations for the variety of 5-dimensional nilpotent Lie algebras [14]}.
All irreducible components of 2-step nilpotent commutative and anticommutative algebras have been described in [13]}, [23]}.
Chouhy proved that in the case of finite-dimensional associative algebras,
the \(N\) -Koszul property is preserved under the degeneration relation [6]}.
Degenerations have also been used to study a level of complexity of an algebra [5]}, [4]}, [27]}.
The study of degenerations of algebras is very rich and closely related to deformation theory, in the sense of Gerstenhaber [28]}.
